# >Finance

Created 7/1/1996
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### Six Lessons of Market Efficiency

Basics:

• Present value of a perpetuity: C/r
• Present value of a growing (or shrinking) perpetuity: C/(r-g)
• Present value of C dollars t years from now: C/[(1+r)t]
• Present value of a C-dollar t-year annuity: C[(1/r)-(1/[r(1+r)t])
• "Rule of 72": (1+r)t = 2 (approximately) whenever rt=.72
• beta = [E((r1-r*1)(rm-r*m)]/[(rm-r*m)2]
• r*i = r*f + betai(r*m-rf)
• Expected return of a portfolio with N securities, a share 1/N invested in each security:
• Standard deviation of a portfolio with N securities, a share 1/N invested in each security:

Corporate Financing and the Six Lessons of Market Efficiency

You've learned how to spend money--how to choose among different potential investment projects. Now let's figure out how to raise it--how firms interface with the capital markets to raise the money to undertake investment projects.

Some sample "capital structure" problems:

pay dividends or retain earnings?

issue stock or issue bonds?

issue short term debt or issue long term debt?

issue "standard" securities or issue "fancy" option-based securities

how to use the financial markets to hedge risk...

We Always Come Back to NPV

The decision to sell a share of stock, and the decision to purchase an electromechanical capital good are basicly similar. Both involve the "valuation" of a risky asset, and the comparison of the value of a risky future stream with a present sum. The fact that one asset is "real" and the other "financial" shouldn't bother you.

The present value of borrowing. Suppose the government agrees to lend your firm \$100,000 for 10 years at an interest rate of 3%:

NPV = +\$100,000 - sum{\$3,000/(1+r)^t} for ten years - \$100,000/(1+r)^10

If the appropriate discount rate is 10%...

= +\$100,000 - \$56,988 = +\$43,012 //when the appropriate discount rate is 10%, an offer to loan you money for 10 years at 3% is truly an amazing deal...

(Use the "rule of 72" to see that it is an amazing deal right off)

• Financing decisions are easier to reverse than investment decisions
• It's much harder to make or lose lots of money by making bad financing decisions...
• In investment decisions, you are not facing a perfect, competitive market
• In financial makets, you are facing a nearly perfect, competitive market
• If selling a security has a positive NPV to you, it probably has a negative NPV to the purchaser. You probably will not find many such purchasers.

If capital markets are efficient, then purchase or sale of any security at the prevailing maket price is never a positive (or negative) NPV transaction...

What Is an "Efficient" Market?

We assume that capital markets are efficient. By "efficient" we mean a bunch of things

• that all relevant and ascertainable information is reflected in the market price already because it is widely and cheaply available to investors.
• Stock prices are a random walk (with drift)
• Weak efficiency: the past pattern of prices doesn't allow you to make money
• Semi-strong. Published information doesn't allow you to make money
• Strong. All the hard work in the world doesn't allow you to make [much] money. One of the senior people on my brother's risk-arb desk, an equity analyst; trailing the S&P 500

There are some conspicuously bad portfolio managers (those who trade a lot, and have high overhead expenses). There are very few consistently good ones...

Let's expand this:

Maurice Kendall: stock prices appeared to be a random walk (with drift). Price changes independent of the most recent price change.

What this means for "technical analysis".

Competition among investment analysts should lead prices to reflect "true values"--true value does not mean future value, but an expected value that incorporates all he information available to investors at that time. If prices always reflect all information, they will only change when new "information" arrives. But by definition we don't know whether new information will be good or bad.

Suppose analysts aren't competitive, and there are predictable cycles: we make money off these cycles--for a while.

• Weak efficiency: the past pattern of prices doesn't allow you to make money
• Semi-strong. Published information doesn't allow you to make money
• Strong. All the hard work in the world doesn't allow you to make [much] money. One of the senior people on my brother's risk-arb desk, an equity analyst; trailing the S&P 500

The crash of '87 as a challenge to the efficient markets hypothesis. What was the news? Response seems to be (a) the market is better at relative prices than at absolute benchmarks, and (b) with P=D/(r-g) only a small shift in g is necessary to produce big shifts in P.

Brealey and Myers believe that the '87 crash does not undermine the evidence for market efficiency with respect to relative prices

No Theory Is Perfect: Anomalies:

Small firm effect--small firm estimated betas are not high enough to account for their high returns

January effect--small firms earn high returns in January (people wait until after the end of the tax year to dump losing positions in big stocks?)//no one knows what is going on...

Long-term patterns--buy when price/dividend ratios are low...

The Six Lessons of Market Efficiency

Lesson 1: Markets have no memory (don't wait for recent price changes to be reversed; they probably will not be)

Lesson 2: Trust market prices (more than your own hunches)

Lesson 3: Look at market prices in detail to predict the future (term structure; market's unfavorable assessment of Viacom's takeover of Paramount; for the market price implicitly weights a lot of people's serious assessments)

Lesson 4: Do not believe in financial illusions (dividends and stock splits; stock prices run up before a split)

Lesson 5: Value is lost when the company does something that a shareholder can do on his own for smaller transaction costs

Lesson 6: Demands for stocks should be highly, highly elastic.

Note that the efficient markets hypothesis does not mean that the financing of a corporation will "take care of itself"; it provides a starting point, not an ending point, for analyis.

Possible quiz: Suppose that you have spent a week researching the business prospects of Apple Computer (it closed at \$25 5/8 yesterday). Suppose that your research suggests a stock price of \$40. Using both pieces of information--your research and the market price--what is your best guess of the value of Apple Computer stock? Which source of information did you weight more heavily? Why?